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At least 253 records · Page 14

Characterizing Response Versus Scan-Angle for MODIS Reflective Solar Bands Using Deep Convective Clouds

MODIS consists of a cross-track, two-sided scan mirror, whose reflectance is not uniform but is a function of angle of incidence (AOI). This feature, known as response versusscan-angle (RVS), was characterized for all reflective solar bands of both MODIS instruments prior to launch. The RVS characteristic has changed on orbit, which must be tracked precisely over time to ensure the quality of MODIS products. The MODIS characterization support team utilizes the onboard calibrators and the earth view responses from multiple pseudo invariant desert sites to track the RVS changes at different AOIs. The drawback of using deserts is the assumption that these sites are radiometrically stable during the monitoring period. In addition, the 16-day orbit repeat cycle of MODIS allows for only a limited set of AOIs over a given desert. We propose a novel and robust approach of characterizing the MODIS RVS using tropical deep convective clouds (DCC). The method tracks the monthly DCC response at specified sets of AOIs to compute the temporal RVS changes. Initial results have shown that the Aqua-MODIS collection 6 band 1 level 1B radiances show considerable residual RVS dependencies, with long-term drifts up to 2.3 at certain AOIs.

Clouds↗

Modeling Systems-Of-Systems Interfaces with SysML

Space data systems are inherently complex. They are systems-of-systems, typically composed of spacecraft and mission operations systems (MOS) belonging to one (or more) organizations, and multi-mission communication assets belonging to other organizations. In many cases, the spacecraft contain sub-systems and instruments provided by different organizations, and MOS systems that may be developed and operated by other organizations. The point of greatest leverage in system architecting is at the interfaces. We have developed a set of methods for using SysML to model systems-of-systems and their interfaces. This paper describes how to apply this method to space data systems at a variety of levels of detail, from abstract systems and subsystems down to hardware and software components, including the details of their interfaces and protocol designs.

Shames, Peter M.↗

Summary of Technical Interchange Meetings (TIMs) Designed to Enable Earth Independent Medical Operations (EIMO)

The Exploration Medical Capability Element (ExMC) in NASA’s Human Research Program hosted a series of TIMs in 2023-2024 designed to stimulate discussion around specific topics with the goal of enabling EIMO. In context of the thematic constituent elements of EIMO, namely pre-mission planning, acute/emergent/prolonged medical decision making, supply/resource management and task load management, subject matter experts from industry, academia and government (NASA and other Agencies) provided valuable and actionable guidance and recommendations. Earth-based medical experts will remain indispensable for pre-mission planning, however, management of acute/emergent medical contingencies will require a gradual transition of medical care and decision making from terrestrial to space-based assets to enable support of astronaut health and performance and reduce overall mission risk. Key to achieving these enhancements is providing an integrated data system platform capable of utilizing multiple data streams in concert with a variety of on-board databases and passive monitoring of video and wearable sensors to enable a multi-modal, agentic AI-based clinical decision support system (CDSS) to support crew medical officer (CMO) medical decision-making. The EIMO series of TIMs (I-V) have proven to be instructive and portend a significant paradigm shift will be necessary to maintain crew health and performance on exploration class missions. Importantly, since the expected paradigm shift will be significantly different from the methods of operation that have been employed for the majority of missions from the inception of human spaceflight to date, any proposed methods must be deployed in the setting of ongoing operations early and be “tested, reviewed and practiced” while reliable back-up is available to facilitate an Enterprise-wide level of comfort and acceptance. Serious constraints on data transmission coupled with a large and expanding universe of on-board medical informatics data streams will necessitate implementation of a CDSS to supplant the current reliance on support provided by ground-based SMEs. Establishment of trust in the system by CMO/crew and the ground-based medical support team will be essential. Co-development of a CDSS with industry partners will assure that state of the art tools can be employed, and industry efficiencies can be leveraged. Training regimens, materials and tools must evolve to be responsive (just-in-time training) and facilitate autonomous execution of procedures. Proficiency metrics should be established and be based on validated competencies or milestones as opposed to a prescribed number of training hours. Training should be prioritized for broad, translatable skills that have universal application across a variety of medical conditions. Repetition was deemed to be the key to achieving proficiency and emphasis should lie in procedural training which is known to extinguish more rapidly than diagnostic skills. Advanced tools, e.g., extended reality, can provide more realistic and effective training. Use of advanced probabilistic risk assessment tools will be essential to optimize the medical system capability while carefully balancing risk relative to mass/power/volume limitations. Importance of factoring use-life of medical supplies and maintaining awareness of redundancy and opportunity to re-purpose under off nominal situations was emphasized. Consideration of adopting optimized performance standards vs. “good-enough” performance thresholds is warranted. The use of legacy systems as opposed to creating new systems may be preferable. Managing task load and associated cognitive load will be essential to maintain operational safety and behavioral health. ExMC aspires to create a shared EIMO paradigm and strategic vision for advancing medical system design through novel technologies, training, protocols, and support capabilities, built upon the spirit of successful strategies and innovations over the past six decades of space medicine operations.

Jay Lemery↗

Multi-fidelity learning for interatomic potentials: low-level forces and high-level energies are all you need

The promise of machine learning interatomic potentials (MLIPs) has led to an abundance of public quantum mechanical (QM) training datasets. The quality of an MLIP is directly limited by the accuracy of the energies and atomic forces in the training dataset. Unfortunately, most of these datasets are computed with relatively low-accuracy QM methods, e.g. density functional theory with a moderate basis set. Due to the increased computational cost of more accurate QM methods, e.g. coupled-cluster theory with a complete basis set (CBS) extrapolation, most high-accuracy datasets are much smaller and often do not contain atomic forces. The lack of high-accuracy atomic forces is quite troubling, as training with force data greatly improves the stability and quality of the MLIP compared to training to energy alone. Because most datasets are computed with a unique level of theory, traditional single-fidelity (SF) learning is not capable of leveraging the vast amounts of published QM data. In this study, we apply multi-fidelity learning (MFL) to train an MLIP to multiple QM datasets of different levels of accuracy, i.e. levels of fidelity. Specifically, we perform three test cases to demonstrate that MFL with both low-level forces and high-level energies yields an extremely accurate MLIP—far more accurate than a SF MLIP trained solely to high-level energies and almost as accurate as a SF MLIP trained directly to high-level energies and forces. Therefore, MFL greatly alleviates the need for generating large and expensive datasets containing high-accuracy atomic forces and allows for more effective training to existing high-accuracy energy-only datasets. Indeed, low-accuracy atomic forces and high-accuracy energies are all that are needed to achieve a high-accuracy MLIP with MFL.

36 MATERIALS SCIENCE↗

Bond Dissociation Energies of the Actinide Halides AnX, An = Ac–Lr and X = F–I, Utilizing Relativistic Composite Coupled Cluster Approaches

Bond dissociation energies (BDEs) have been calculated for the set of actinide halides AnX with An=Ac, Pa, and Np-Lr and X=F-I. Two composite thermochemistry methods based on the Feller-Peterson-Dixon (FPD) approach have been utilized, one involving spinor-based relativistic CCSD(T) calculations where spin-orbit (SO) was included at the orbital level and another using scalar relativistic CCSD(T) with a posteriori SO contributions based on 2-component multireference configuration interaction calculations. The method that was chosen for a given actinide halide was based on which representation yielded the best single determinant reference determinant for the coupled cluster calculation. The spinor-based method was chosen for all cases except for AmX, CmX, and BkX. Both composite approaches included contributions accounting for basis set truncation, outer-core correlation, the Gaunt interaction, and QED. The scalar FPD results, as well as the spinor-based calculations for AcF, also included higher order electron correlation up through CCSDT(Q). In addition to BDEs, CCSD(T) equilibrium bond lengths, harmonic frequencies, and vibrational anharmonicity constants are reported for all species. Last, the FPD BDEs for the fluorides were used to confirm the trend across the actinide series previously predicted by Gibson using bonding models based atomic promotion energies that provide a single 6d electron for bonding. In particular the local minimum in the BDEs at AmF is confirmed in the present calculations. Furthermore, the BDEs for LrX are predicted to be slightly larger than those of AcX, making them the largest in the actinide halide series.

Actinides↗

Random coordinate descent: A simple alternative for optimizing parameterized quantum circuits

Variational quantum algorithms rely on the optimization of parameterized quantum circuits in noisy settings. The commonly used back-propagation procedure in classical machine learning is not directly applicable in this setting due to the collapse of quantum states after measurements. Thus, gradient estimations constitute a significant overhead in a gradient-based optimization of such quantum circuits. This paper introduces a random coordinate descent algorithm as a practical and easy-to-implement alternative to the full gradient descent algorithm. This algorithm only requires one partial derivative at each iteration. Motivated by the behavior of measurement noise in the practical optimization of parameterized quantum circuits, this paper presents an optimization problem setting that is amenable to analysis. Under this setting, the random coordinate descent algorithm exhibits the same level of stochastic stability as the full gradient approach, making it as resilient to noise. The complexity of the random coordinate descent method is generally no worse than that of the gradient descent and can be much better for various quantum optimization problems with anisotropic Lipschitz constants. Theoretical analysis and extensive numerical experiments validate our findings. Published by the American Physical Society 2024

Ding, Zhiyan (ORCID:000000018863403X)↗

Atmospheric observations for STS-3 landing

Synoptic weather conditions existing over the western United States for the time of Shuttle descent are presented. The techniques and methods used to furnish synoptic atmospheric data at the surface and aloft for flight verification of the STS 3 orbiter during its descent are specified. Examples of the upper level data set are given.

Turner, R. E.↗

Three-dimensional blade vortex interactions

A three-dimensional time dependent Navier-Stokes analysis was applied to the rotor blade vortex interaction problem. The numerical procedure is an iterative implicit procedure using three point central differences to represent spatial derivatives. A series of calculations were made to determine the time steps, pseudo-time steps, iterations, artificial dissipation level, etc. required to maintain a nondissipative vortex. Results show the chosen method to have excellent non-dissipative properties provided the correct parameters are chosen. This study was used to set parameters for both two- and three-dimensional blade vortex interaction studies. The case considered was the interaction between a vortex and a NACA0012 airfoil. The results showed the detailed physics during the interaction including the pressure pulse propagating from the blade. The simulated flow physics was qualitatively similar to that experimentally observed. The BVI phenomena is the result of the buildup and violent collapse of the shock waves and local supersonic pockets on the blade surfaces. The resulting pressure pulse build-up appears to be centered at the blade leading edge.

Davoudzadeh, Farhad↗

Two- and three-dimensional blade vortex interactions

A three-dimensional time dependent Navier-Stokes analysis was applied to the rotor blade vortex interaction (BVI) problem. The numerical procedure is an iterative implicit procedure using three point central differences to represent spatial derivatives. A series of calculations were made to determine the time steps, pseudo-time steps, iterations, artificial dissipation level, etc. required to maintain a nondissipative vortex. Results show the chosen method to have excellent non-dissipative properties provided the correct parameters are chosen. This study was used to set parameters for both two- and three-dimensional blade vortex interaction studies. The two-dimensional study considered the interaction between a vortex and a NACA0012 airfoil. The results showed the detailed physics during the interaction including the pressure pulse propagating from the blade. The simulated flow physics was qualitatively similar to that experimentally observed. The 2-D BVI phenomena is the result of the buildup and violent collapse of the shock waves and local supersonic pockets on the blade surfaces. The resulting pressure pulse build-up appears to be centered at the blade leading edge. The three-dimensional interaction study considered the case of a vortex at 20 deg incidence to the blade leading edge. Although the qualitative results were similar to that of the two-dimensional interaction, details clearly showed the three-dimensional nature of the interaction process.

Davoudzadeh, F.↗

Cryogenic Fluid Management Technology Development Roadmaps

Advancement in Cryogenic Fluid Management (CFM) Technologies is essential for achieving NASA's future long duration missions. Propulsion systems utilizing cryogens are necessary to achieve mission success. Current State Of the Art (SOA) CFM technologies enable cryogenic propellants to be stored for several hours. However, some envisioned mission architectures require cryogens to be stored for two years or longer. The fundamental roles of CFM technologies are long term storage of cryogens, propellant tank pressure control and propellant delivery. In the presence of heat, the cryogens will "boil-off" over time resulting in excessive pressure buildup, off-nominal propellant conditions, and propellant loss. To achieve long term storage and tank pressure control, the CFM elements will intercept and/or remove any heat from the propulsion system. All functions are required to perform both with and without the presence of a gravitational field. Which CFM technologies are required is a function of the cryogens used, mission architecture, vehicle design and propellant tank size. To enable NASA's crewed mission to the Martian surface, a total of seventeen CFM technologies have been identified to support an In-Space Stage and a Lander/Ascent Vehicle. Recognizing that FY2020 includes a Decision Point regarding the In-Space Stage Architecture, a set of CFM Technology Development Roadmaps have been created identifying the current Technology Readiness Level (TRL) of each element, current technology "gaps", and existing technology development efforts. The roadmaps include a methodical approach and schedule to achieve a flight demonstration in FY2023, hence maturing CFM technologies to TRL 7 for infusion into the In-Space Stage Preliminary Design.

Stephens, J. R.↗

NASA's Cryogenic Fluid Management Technology Development Roadmaps

The maturation of Cryogenic Fluid Management (CFM) Technologies is essential for achieving NASA's future long duration missions. Propulsion systems utilizing cryogens are necessary to achieve NASA's exploration missions to the moon, Mars, and beyond. Current State Of the Art (SOA) CFM technologies enable cryogenic propellants to be stored for several hours prior to their use. However, some envisioned mission architectures require that cryogens to be stored for two years or longer. The fundamental roles of CFM technologies are long term storage of cryogens, propellant tank pressure control and propellant delivery. In the presence of heat, the cryogens will "boil-off" over time resulting in excessive pressure buildup, off-nominal propellant conditions for engine consumption, and propellant loss. To achieve long term storage and tank pressure control, the CFM elements will intercept and/or remove any heat from the propulsion system. All functions are required to be performed both with and without the presence of a gravitational field. Which CFM technologies are required is a function of the cryogens used, mission architecture, vehicle design and propellant tank size. To enable NASA's crewed missions beyond Low Earth Orbit, a total of twenty-seven CFM technologies have been identified to support various In-Space Stages and Lander/Ascent Vehicles. A set of CFM Technology Development Roadmaps have been created identifying the current Technology Readiness Level (TRL) of each element, current technology "gaps", and existing technology development efforts. The roadmaps include a methodical approach and schedule to achieve a flight demonstration, hence maturing CFM technologies to TRL 6/7 for infusion into the NASA's exploration elements. Additionally, a survey of the aerospace industry was completed to understand their views on the various technologies and how they would be infused. This does not cover all possible technologies, but rather those that are of interest to NASA specifically.

Cryogenic fluid management↗

Towards Integrated Computational Materials Engineering for Quantifying Performance Impacts of Microstructure and Defect Interactions in Powder Bed Fusion Parts

Powder bed fusion (PBF) additive manufacturing (AM) enables the creation of parts with complexity and functionality levels that were previously impossible with traditional manufacturing methods. By modifying the laser power, hatch spacing, or the numerous other processing parameters, the PBF process supports the production of a wide set of materials and geometries. However, that same process parameter design flexibility causes the process-design space of PBF to be massive and expensive to explore experimentally. Another challenge is quality variation across a build. As a part is being built, geometric variance between locations, such as at a thin-wall section vs. the bulk material, may cause the specified processing parameters to no longer be acceptable for producing defect-free printing. Furthermore, if the processing parameters deviate during the print process, it is difficult to assess if the part will still perform satisfactorily. Integrated Computational Materials Engineering (ICME) provides a way to understand and address these various challenges. This talk will present advancements in process-structure simulations of PBF at NASA Langley Research Center. The ability to simulate grain-scale PBF microstructures using the Physically Based Monte Carlo method will be demonstrated and compared to experimental measurements. Techniques for simulating three-dimensional lack-of-fusion and keyhole porosity defects based on the specific processing conditions and approaches for integrating the two porosity prediction techniques alongside the computational microstructure evolution models will be shown. Finally, the integration of simulated PBF microstructures, embedded process defects, and crystal plasticity finite element models to elucidate the interaction of porosity and microstructure on micromechanical fields will be demonstrated. These integrated techniques demonstrate an example of using ICME to relate processing to performance for PBF AM materials. With continued maturity, it is hoped that such ICME approaches will lead to next-generation computational-materials supported qualification and certification of AM parts.

Additive manufacturing↗

VARI3D & PERSENT: Perturbation and Sensitivity Analysis

The nodal diffusion method is one of the most widely used approaches in modern reactor analysis. In the nodal diffusion method, a coarse multi-group set of “homogenized” parameters is constructed such that the complex geometry of a reactor core along with the energy dependence of neutron and gamma ray cross sections in a nuclear reactor are conserved in the simpler geometry. The homogenization is typically done on a fuel assembly level as is the case in the DIF3D code developed at Argonne National Laboratory. The nodal methodology is used primarily to predict fuel cycle behavior of nuclear systems of which there is a substantial amount of validation in the literature. Another use of the nodal method is to obtain reactivity coefficients and kinetics parameters for use in a safety analysis of a given nuclear reactor. While there are many ways to obtain reactivity worth and kinetics parameters, the work presented in this manuscript is unique as it provides the user with the ability to compute reactivity worths, kinetics parameters, and cross section sensitivities with a Cartesian and hexagonal geometry based transport code. This manuscript serves as a single manual for two separate codes: VARI3D and PERSENT. The VARI3D code (VARIational 3D) is based upon the classic finite difference diffusion theory solver available in DIF3D. The PERSENT code (PERturbation and SENitivity for Transport) is based upon the variational nodal method employed in DIF3D termed VARIANT. The VARIANT solver was added to DIF3D in 1995 and has seen continued development and use for the last 18 years. Because VARI3D primarily uses deprecated coding practices, rather than incorporating the perturbation and sensitivity treatments for transport within VARI3D, a new coding development was built using modern Fortran coding. The primary purpose of this manual is to describe the theory behind PERSENT (and by convenience, that of VARI3D) and discuss the input and output of PERSENT along with giving potential users an idea of how to use it. While this manuscript does describe the input and output of VARI3D, the PERSENT code is intended to be the replacement capability of VARI3D as PERSENT can generate nearly identical (if not superior) diffusion theory results. In this manuscript, the relevant aspects of generalized perturbation theory and exact perturbation theory that apply to both VARI3D and PERSENT are covered. The input and output of VARI3D is displayed by excerpting several of the example problems. Similarly, the input and output of PERSENT is displayed along with tips on how best to use the code. Note that the input and output of the inhomogeneous solver wrapped around DIF3D (DIF3D_IFS) is also discussed as it is needed to carry out some of the sensitivities in PERSENT such as reaction rate ratios. This manuscript describes several perturbation and sensitivity problems, and the results computed using PERSENT. From these sections, potential users should find that PERSENT provides not only the typical tables of numbers desired in perturbation and sensitivity analysis work, but also can visually plot the result for a more thorough understanding of the space and energy distribution (Section 5). Overall, PERSENT is observed to produce accurate reactivity worths and sensitivities for the displayed set of test problems and clearly demonstrates the need to have a transport-based sensitivity capability as evident from the thousands of percent errors observed in the 21-group hexagonal fast reactor problem (covered in Section 7). The uncertainty calculation capability is described in Section 3 and demonstrated in Section 7.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Custom Accessors: Enabling Scalable Data Ingestion, (Re-)Organization, and Analysis on Distributed Systems

The emerging class of high velocity and high volume data analytic workflows comprise interwoven data ingestion, organization, and processing stages, with ingestion and organization steps often contributing comparable or even higher computational costs than actual processing steps. Since complex workflows consist of a variety of phases that view and use data differently, being able to construct efficient, scalable, distributed data structures (arrays, vectors, sets, maps, and multi-maps) is essential and requires custom methods to extend and shrink containers, analyze and position data, and, maintain globallyconsistent meta-data. In this paper, we propose a novel datastructure access paradigm based on the concept of Accessors. At a high level, accessors are customizable callable objects that can modify the behavior of insert, read, update, and delete operations for distributed containers while preserving atomicity guarantees. Accessors provide a very clean and natural way to implement a variety of programming patterns, e.g., conditional insertion/deletion and cascading computations, which would be otherwise hard (or even impossible) to express in parallel and distributed settings without using locks. We demonstrate the practicality and usefulness of our approach with two representative use cases and study the performance of these applications on a distributed High-Performance Computing system. Our analysis highlights that our proposed abstraction allows for an effective overlapping and concurrent execution of different workflow steps (e.g., data ingestion and analysis), which in a conventional analytics pipeline would execute sequentially, contributing cumulatively to the overall latency.

Castellana, Vito G. [BATTELLE (PACIFIC NW LAB)] (O↗

Predicting motion sickness during parabolic flight

BACKGROUND: There are large individual differences in susceptibility to motion sickness. Attempts to predict who will become motion sick have had limited success. In the present study, we examined gender differences in resting levels of salivary amylase and total protein, cardiac interbeat intervals (R-R intervals), and a sympathovagal index and evaluated their potential to correctly classify individuals into two motion sickness severity groups. METHODS: Sixteen subjects (10 men and 6 women) flew four sets of 10 parabolas aboard NASA's KC-135 aircraft. Saliva samples for amylase and total protein were collected preflight on the day of the flight and motion sickness symptoms were recorded during each parabola. Cardiovascular parameters were collected in the supine position 1-5 days before the flight. RESULTS: There were no significant gender differences in sickness severity or any of the other variables mentioned above. Discriminant analysis using salivary amylase, R-R intervals and the sympathovagal index produced a significant Wilks' lambda coefficient of 0.36, p=0.006. The analysis correctly classified 87% of the subjects into the none-mild sickness or the moderate-severe sickness group. CONCLUSIONS: The linear combination of resting levels of salivary amylase, high-frequency R-R interval levels, and a sympathovagal index may be useful in predicting motion sickness severity.

manned↗

Predicting Motion Sickness During Parabolic Flight

Background: There are large individual differences in susceptibility to motion sickness. Attempts to predict who will become motion sick have had limited success. In the present study we examined gender differences in resting levels of salivary amylase and total protein, cardiac interbeat intervals (R-R intervals), and a sympathovagal index and evaluated their potential to correctly classify individuals into two motion sickness severity groups. Methods: Sixteen subjects (10 men and 6 women) flew 4 sets of 10 parabolas aboard NASA's KC-135 aircraft. Saliva samples for amylase and total protein were collected preflight on the day of the flight and motion sickness symptoms were recorded during each parabola. Cardiovascular parameters were collected in the supine position 1-5 days prior to the flight. Results: There were no significant gender differences in sickness severity or any of the other variables mentioned above. Discriminant analysis using salivary amylase, R-R intervals and the sympathovagal index produced a significant Wilks' lambda coefficient of 0.36, p= 0.006. The analysis correctly classified 87% of the subjects into the none-mild sickness or the moderate-severe sickness group. Conclusions: The linear combination of resting levels of salivary amylase, high frequency R-R interval levels, and a sympathovagal index may be useful in predicting motion sickness severity.

Harm, Deborah L.↗

Engineering Polyketide Stereocenters with Ketoreductase Domain Exchanges

Polyketide synthases (PKSs) are versatile biosynthetic megasynthases capable of producing a diverse range of natural products with many applications, including in pharmaceuticals. The stereochemical precision of PKSs makes them a powerful tool for engineering tailored, unnatural polyketides; however, modifying the stereocenters of a PKS product while maintaining production levels remains a significant challenge. In this study, we systematically tested and evaluated strategies for ketoreductase (KR) domain exchanges, the domain responsible for setting stereocenters of polyketide products. After first optimizing the method for KR exchanges, we then performed 44 KR domain exchanges on three different PKSs to obtain high production of all four stereoisomers in vivo. By testing both one- and two-module PKS systems, we investigated how downstream modules process intermediates with altered stereochemistry and found that the configuration of the α-substituents was critical for gatekeeping by the ketosynthase (KS). To overcome this constraint, we investigated two different strategies for altering the KS domain, including introducing targeted mutations in the downstream KS, and exploring boundaries in exchanging the entire functional unit from the donor PKS. Both strategies successfully modified the KS stereocontrol with distinct trade-offs; the functional unit exchange resulted in higher titer improvements, though it was more likely to break the entire PKS. This study demonstrates a comprehensive approach to successfully engineering all four stereochemical configurations in multiple PKS systems, advancing our understanding of and ability to rationally modify polyketide stereochemistry through multiple engineering strategies.

Keiser, Leah S. [Joint BioEnergy Institute (JBEI),↗

Computation of Jupiter interior models from gravitational inversion theory

Spacecraft measurements of Jupiter have provided the mass, standard pressure level radius, rotation law, internal mass distribution multipole moments, and internal composition and temperature distribution constraints, for the present implementation of a method for deriving planetary interior models that exactly satisfy a set of N gravitational constraints by means of appropriate iteration. The models are not forced to fit the more indirectly derived constraints, which are instead used as conistency checks. In the case of an He mass fraction in the envelope Y of 0.2, the inferred pressure at a mass density of about 0.2 g/cu cm is about a factor of 2 higher than would be indicated by experimental H compression data in the relevant pressure range of 100,000 to one million bar. The inferred pressure distribution is in better agreement with the shock data for a nominal Y value of 0.3 + or - 0.05.

Hubbard, W. B.↗